Aren't you really just talking about the level of abstraction being applied? If there are infinite possibilities between zero and one, then it's just our way of relating to it that imposes the perception of a limitation.
Maybe you can theoretically encode arbitrary (but not infinite) information, but there are still discrete underlying states.
Terrence Howard is that you?
No. You might be reading into it a little bit too much. My point was that finding three needs to be possible for you to find it. If you are looking on the interval 0-1, it is not possible. As other comments have kinda of suggested, you could map every integer to a real and find "three" but if you are going to do that, why not just look on an interval that actually contains the number?